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\begin{document}
\title{Lab 3: Multi Angle Spectrophotometer}
\author{Alexandra Booth \and Glenn Sweeney}

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\maketitle

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\section{Introduction}

Spectophotometry is a specific application of spectroradiometery.

In spectroradiometry, an instrument is used to measure the absolute amount of radiation emitted by an object.
However, when considering reflecting or transmitting materials, this radiation is dependent on both the illuminating source and the intrinsic properties of the material.

Spectrophotometry is nothing more than the measurement of an object reflecting or transmitting light when the source and measurement geometry is well defined.
In these cases, the intrinsic reflectance or transmittance of the material can be measured by dividing the influence of the light source spectrum out of the measurement.
Of course, careful design and calibration is required for such a system, but at the most basic level it is just a carefully constructed spectroradiometric measurement.

Even though spectrophotometry is just an application of a spectroradiometer, spectrophotometers are generally less complicated and less expensive than spectroradiometers.
This is because the source intensity and measurement geometry can be strictly defined and controlled at the time of manufacture.
This in turn generally means that less expensive detectors and optics are needed, because imperfections can be corrected with careful calibration for the specific application.

Reflecting materials rarely have isotropic surface properties. As a result, the geometry of illumination and measurement has a very large effect on the measurements of intrinsic characteristics.
Devices called spectrogoniometers attempt to avoid this problem by capturing a massive set of measurement geometries---however, these instruments are extremely expensive, very slow to take a measurement, and interpretation of measurement results can be almost impossible.

In this lab, a compromise between the spectrophotomer and the spectrogoniometer is considered.
This device, called a multiple angle spectrophotometer, captures a small set of spectrophotometric measurements.
The illumination and all measurements are taken on a plane perpendicular to the measurement surface. The light source is at 45 degrees between the surface and the surface normal. 

For each angle, spectral reflectance is given. This allows a user to quickly understand the characteristics of the material over a broad range of reflectance angles, without being overwhelmed by the data from a spectrogoniometer.

In this lab, we consider the measurement of several different surfaces and compare and contrast the differences between them.
The usefulness of multiple angles of data is also examined.

\section{Procedure}

For this lab, several different samples were measured with the multiple angle spectrophotometer.

First, three different surfaces of Camson paper were considered.
For each surface, a red, green, and blue sample were measured.

The device automatically averages three measurements.
These measurements were taken without replacement.
The backing used during measurement was not controlled, though the samples were all thick enough that the effects of a backing were minimal.

After the paper samples were measured, a set of metal surfaces were considered.
These were sheets of metal with different enamel coatings on top of the metal substrate.
The coatings were all made with the same pigments, but had different surface characteristics.
These were compared and contrasted with the instrument.

\section{Results}

Figures \ref{fig:red_spectra}, \ref{fig:green_spectra}, and \ref{fig:blue_spectra} present the spectral reflectance curves for three different paper surfaces (denoted by different symbols) at a variety of measurement angles.
Immediately, several trends are noticable in these plots.
For each color, a single curve shape is apparent across all surfaces and all measurement angles.
This is expected, and it relates to the intrinsic reflectance of the dye set used to manufacture the paper.
However, each surface has different measured reflectance factor values at the same angle, and every set also varies by angle.

One very interesting observation is that without fail, overall reflectance decreases with increasing angle from the illumination.
Also of note however is that -15 degrees always had significantly higher reflectance than 15 degrees.
These two trends are difficult to understand without more information about the functioning of the device and the calculations performed to extract the spectra.
Several possible factors could contribute to the lessening of reflectance at angles further from the source.
The first factor to consider is the measurement geometry itself.
Most materials reflect a specular component, which is a mirrorlike reflection off of the surface of the material.
Depending on the surface, this can be very directional, or somewhat less so.
In some cases, it can be nearly nonexistant.
However, because illumination is at 45 degrees, the specular component would normally be measurable at 90 degrees from the illumination.

\begin{figure}
\centering
\includegraphics[width=0.6\textwidth]{blue_spectra.eps}
\caption{Spectra for the three different blue paper surfaces at different angles. Each shape identifies one of the three types of papers.  The triangle denotes paper samples 40x. The square denotes the brut paper samples. The circle denotes the 80alpha paper samples. Each symbol color represents a different measurement angle, with red, green, blue, cyan, magenta, yellow corresponding to -15, 15, 25, 47, 75, 110 degrees, respectively.}
\label{fig:blue_spectra}
\end{figure}


\begin{figure}
\centering
\includegraphics[width=0.6\textwidth]{green_spectra.eps}
\caption{Spectra for the three different green paper surfaces at different angles.  The triangle denotes paper samples 40x. The square denotes the brut paper samples. The circle denotes the 80alpha paper samples.  Each symbol color represents a different measurement angle, with red, green, blue, cyan, magenta, yellow corresponding to -15, 15, 25, 47, 75, 110 degrees, respectively.}
\label{fig:green_spectra}
\end{figure}


\begin{figure}
\centering
\includegraphics[width=0.6\textwidth]{red_spectra.eps}
\caption{Spectra for the three different red paper surfaces at different angles.  The triangle denotes paper samples 40x. The square denotes the brut paper samples. The circle denotes the 80alpha paper samples.  Each symbol color represents a different measurement angle, with red, green, blue, cyan, magenta, yellow corresponding to -15, 15, 25, 47, 75, 110 degrees, respectively.}
\label{fig:red_spectra}
\end{figure}

A second possibility for this falloff is the geometry of light itself.
When light hits a surface, the amount of irradiance is variant on the angle of incidence.
Furthermore, the exitance from the surface decreases with the angle of exitance considered.
If one of these sources of radiation decrease are not accounted for in the calibration of the device, it is definitely possible that as measurement angles become large, the overall reflectance factor measured would appear to be small.

Another observation of note on the spectral plots is the high reflectance factors measured at some of the small angles of deviation.
Materials cannot reflect more than 100\% of the incident light (though some processes such as fluorescence may create measurements over 100\%.
However, the measured curves in many places extend well past 100\%.
This is because this device measures reflectance {\it factor}, which does not correspond directly to reflectance.
Instead, reflectance factor is the ratio of light reflected compared to the amount of light reflected by a perfect reflecting diffuser.
This is generally a very good way to consider reflectance.
However, in cases where the reflecting material is not diffuse, it is possible to measure reflectance factors over 100\%, such as in this case.
This simply means that due to the reflectance geometry of the sample, more radiation was exitant in the direction of measurement for the patch than for the perfect reflecting diffusor.

To have a more intuitive visualization of the color information for the Camson papers, the spectra were converted to x-y chromaticities using the CIE standard illuminant D65 and the 10 degree observer.
These were suggested by the manufacturer.
Figure \ref{fig:paper_xy} shows the results of these calculations.
The most noticable trend in this data is that for every paper and every measurement angle, the chromaticities form a perfect line. 
Because these lines point towards the white point used for calculation, this means that the dominant wavelength (which can be thought of as an expression of hue) does not change for the dye set.
Instead, only the purity changes.
This is a very interesting discovery, because it means every paper with the same dye set has the same fundamental color, and instead just has different proportions of the light source mixed in.
This could be because of the specular reflectance of each paper.
A specular reflectance does not carry with it any information about the material it reflected off of---it has the same spectral signature as the source.
So, for angles with a higher specular component more source would be present, and thus the purity (and chroma) would decrease accordingly.

\begin{figure}
\centering
\includegraphics[width=0.6\textwidth]{paper_xy.eps}
\caption{x-y chromaticities for the paper samples. Note that regardless of sample (denoted by different symbols), the dominant wavelength remains unchanged. The triangle denotes paper samples 40x. The cross denotes the brut paper samples. The circle denotes the 80alpha paper samples. }
\label{fig:paper_xy}
\end{figure}

To confirm these results, the colors were plotted in yet another color space.
Figure \ref{fig:paper_lab} shows the papers drawn in the a*b* chromaticity space.
This is a uniform color space that attempts to make measurements of color differenes correlate to the human visual system.
Again, each color, regardless of surface, clusters for each dye appear in a straight line.
These lines more or less point towards the origin, which is neutral. Because of this, it means that the papers are approximately of constant hue regardless of viewing angle or surface - the only difference is chroma.

\begin{figure}
\centering
\includegraphics[width=0.6\textwidth]{paper_lab.eps}
\caption{a*b* plot for the different paper surfaces. The triangle denotes paper samples 40x. The cross denotes the brut paper samples. The circle denotes the 80alpha paper samples. }
\label{fig:paper_lab}
\end{figure}

The same process was performed for black metallic samples.
Each sample had a different surface texture over an identical pigment layer. 
The spectral curves are shown in Figure \ref{fig:metal_spectra}.
As before, there is a change in the reflectance based on viewing angle. Larger viewing angles always measure less light.
Also, there is still a characteristic shape.

\begin{figure}
\centering
\includegraphics[width=0.6\textwidth]{metal_spectra.eps}
\caption{Spetral curves for the metal samples at different viewing angles. The triangle denotes the glossy surface. The square denotes the pearlescent surface. The circle denotes the rough surface.  Each symbol color represents a different measurement angle, with red, green, blue, cyan, magenta, yellow corresponding to -15, 15, 25, 47, 75, 110 degrees, respectively.}
\label{fig:metal_spectra}
\end{figure}

The metal samples plotted in the x-y chromaticity space are much less interesting.
See Figure \ref{fig:metal_xy} for why. 
Because the black patches were already (almost) achromatic, there was no noticable difference in the patch chromaticities as a function of surface or measurement angle.

\begin{figure}
\centering
\includegraphics[width=0.6\textwidth]{metal_xy.eps}
\caption{x-y chromaticities for the metal surfaces. Regardless of surface and viewing angle, the chromaticity remained unchanged. The triangle denotes the glossy surface. The cross denotes the pearlescent surface. The circle denotes the rough surface.}
\label{fig:metal_xy}
\end{figure}


After all of this, is there any way to characterize the differences in surfaces with such a system?
The best answer the experimenters could arrive at is ``sort of''.
The very coarse measurement angles of the device make it impossible to measure and quantify all of the radiation leaving the sample.
However, some information can still be recovered about the relative surface properties.
Figure \ref{fig:l_trend} shows the L* value of each sample as a function of angle.
As previously discussed, this vaue decreases for larger angles.
However, tehre is also an interesting trend that for every set of samples, there is a point at which the lightest patch becomes the darkest patch.
This turnover is interesting, because it hints at a different falloff for each patch.
There is not enough information here to reach any meaningful conclusions about what this could mean, but it is possible that the location of this point may give some information about the material surface properties.



\begin{figure}
\centering
\includegraphics[width=0.6\textwidth]{l_trend.eps}
\caption{L* for each sample by viewing angle.}
\label{fig:l_trend}
\end{figure}

\FloatBarrier


\section{Analysis and Conclusions}

Surface characteristic analysis is not simple with only a few narrow measuring angles.
Better results could have been obtained if the reflectance characteristic had been measured on many more angles.
Then, a reflectance profile could have been constructed and compared for each surface.
Also, the lack of a measurement on the specular reflectance angle makes comparing the specularity of each sample inconvenient.

The multiple angle spectrophotometer seems more suited for applications where the appearance properties of the material changes dramatically for various viewing conditions.
An example of such a material might be a two-tone car paint, where polarized metallic flakes reflect different colors in different directions. However, for relatively uniform surfaces, the measurement instrument was not extremely useful for determining surface characteristics.

\end{document}
